The current price of a non-dividend-paying stock is 30. The volatility of the stock is 0.3 per annum. The risk free rate is 0.05 for all maturities. Using the Cox-Ross-Rubinstein binomial tree model with two time steps to do the valuation, what is the value of a European call option with a strike price of 32 that expires in 6 months? (Your answer should be in the unit of dollar (up to the precision of cents), but without the dollar sign. For example, if your answer is $1.02, just enter 1.02. Please also think whether your answer will be different if the option is an American option.)
Details provided : risk free rate = 5%, current price = 30, volatility = 30%, 6 month European call option = 32, t = 3/12 - since this is a two step binomial tree
Solution:
u = e^(volatility*squareroot(time)) = 1.16183
d = 1/u = 0.86
a = e^rt = 1.012578
p = (a-d)/(u-d) = 0.504343
Call price = 3.315
The current price of a non-dividend-paying stock is 30. The volatility of the stock is 0.3...
The current price of a non-dividend-paying stock is 30. The volatility of the stock is 0.3 per annum. The risk free rate is 0.05 for all maturities. Using the Cox-Ross-Rubinstein binomial tree model with two time steps to do the valuation, what is the value of a European call option with a strike price of 32 that expires in 6 months?
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